Finite Math Examples

$3 x \cdot 1 + x \cdot 2 = 63$ , $x \cdot 1 + x \cdot 2 = 22$ , $x \cdot 1 + 3 x \cdot 2 = 30$

Step 1

Divide each term in $5 x = 63$ by $5$ and simplify.

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Step 1.1

Divide each term in $5 x = 63$ by $5$ .

$\frac{5 x}{5} = \frac{63}{5}$

$3 \cdot x = 22$

$7 x = 30$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $5$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{5 x}{5} = \frac{63}{5}$

$3 \cdot x = 22$

$7 x = 30$

Step 1.2.1.2

Divide $x$ by $1$ .

$x = \frac{63}{5}$

$3 \cdot x = 22$

$7 x = 30$

$x = \frac{63}{5}$

$3 \cdot x = 22$

$7 x = 30$

$x = \frac{63}{5}$

$3 \cdot x = 22$

$7 x = 30$

$x = \frac{63}{5}$

$3 \cdot x = 22$

$7 x = 30$

Step 2

Replace all occurrences of $x$ with $\frac{63}{5}$ in each equation.

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Step 2.1

Replace all occurrences of $x$ in $3 \cdot x = 22$ with $\frac{63}{5}$ .

$3 \cdot (\frac{63}{5}) = 22$

$x = \frac{63}{5}$

$7 x = 30$

Step 2.2

Simplify the left side.

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Step 2.2.1

Multiply $3 (\frac{63}{5})$ .

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Step 2.2.1.1

Combine $3$ and $\frac{63}{5}$ .

$\frac{3 \cdot 63}{5} = 22$

$x = \frac{63}{5}$

$7 x = 30$

Step 2.2.1.2

Multiply $3$ by $63$ .

$\frac{189}{5} = 22$

$x = \frac{63}{5}$

$7 x = 30$

$\frac{189}{5} = 22$

$x = \frac{63}{5}$

$7 x = 30$

$\frac{189}{5} = 22$

$x = \frac{63}{5}$

$7 x = 30$

Step 2.3

Replace all occurrences of $x$ in $7 x = 30$ with $\frac{63}{5}$ .

$7 (\frac{63}{5}) = 30$

$\frac{189}{5} = 22$

$x = \frac{63}{5}$

Step 2.4

Simplify the left side.

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Step 2.4.1

Multiply $7 (\frac{63}{5})$ .

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Step 2.4.1.1

Combine $7$ and $\frac{63}{5}$ .

$\frac{7 \cdot 63}{5} = 30$

$\frac{189}{5} = 22$

$x = \frac{63}{5}$

Step 2.4.1.2

Multiply $7$ by $63$ .

$\frac{441}{5} = 30$

$\frac{189}{5} = 22$

$x = \frac{63}{5}$

$\frac{441}{5} = 30$

$\frac{189}{5} = 22$

$x = \frac{63}{5}$

$\frac{441}{5} = 30$

$\frac{189}{5} = 22$

$x = \frac{63}{5}$

$\frac{441}{5} = 30$

$\frac{189}{5} = 22$

$x = \frac{63}{5}$

Step 3

Since $\frac{441}{5} = 30$ is not true, there is no solution.

No solution

Step 4